Quantitative behavior of unipotent flows and an effective avoidance principle
Quantitative behavior of unipotent flows and an effective avoidance principle
复制标题
单能流的定量行为和有效回避原则
DOI：
10.1007/s11854-023-0309-9
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
N. Shah
中科院分区：
文献类型：
--
作者：
E. Lindenstrauss;A. Mohammadi;G. Margulis;N. Shah
我们给出了幂幺群U在算术商G/\Gamma$上的时间轨道能在G/\Gamma $的齐次子簇附近停留多少的一个有效界，该齐次子簇对应于G的Q-子群。特别是，我们表明，如果这样的U轨道是适度接近适当的齐次子品种的G/\Gamma$很长一段时间，它是非常接近一个不同的齐次子品种。我们的工作建立在Dani和Margulis的线性化方法的基础上。
我们的动机在发展这些界限是为了证明定量密度陈述的幂幺轨道，我们计划在随后的论文中进行。我们的有效界的新的定性影响也给出了。
We give an effective bound on how much time orbits of a unipotent group $U$ on an arithmetic quotient $G/\Gamma$ can stay near homogeneous subvarieties of $G /\Gamma$ corresponding to $\mathbb Q$-subgroups of $G$. In particular, we show that if such a $U$-orbit is moderately near a proper homogeneous subvariety of $G/\Gamma$ for a long time it is very near a different homogeneous subvariety. Our work builds upon the linearization method of Dani and Margulis.
Our motivation in developing these bounds is in order to prove quantitative density statements about unipotent orbits, which we plan to pursue in a subsequent paper. New qualitative implications of our effective bounds are also given.
均匀空间的直径：一个有效的解释
影响因子：
1.4
作者：
Mohammadi, A.;Golsefidy, A. Salehi;Thilmany, F.
通讯作者：
Thilmany, F.